Searching for Diophantine quintuples
Volume 173 / 2016
Acta Arithmetica 173 (2016), 365-382
MSC: Primary 11D09; Secondary 11B37, 11J86, 11D45.
DOI: 10.4064/aa8254-2-2016
Published online: 18 May 2016
Abstract
We consider Diophantine quintuples $\{a, b, c, d, e\}$. These are sets of positive integers, the product of any two elements of which is one less than a perfect square. It is conjectured that there are no Diophantine quintuples; we improve on current estimates to show that there are at most $5.441\cdot 10^{26}$ Diophantine quintuples.
